For international students applying for graduate studies in the United States, a TOEFL score is usually a requirement. However, unlike the GRE score, the TOEFL score hardly carries any weightage in the admission decision. While universities might have a cut-off score, the actual score doesn't matter as long as the candidate clears the cut-off. In fact, it is almost never the case that a candidate is rejected solely on the grounds of a poor TOEFL score.

The purpose of the TOEFL test is to assess the student's proficiency in English, as it is the language of instruction in most graduate programs. However, the admission committee places greater emphasis on other aspects of the application, such as the academic record, research experience, statement of purpose, and letters of recommendation. In some cases, when the TOEFL score is low, but the rest of the application is strong, the candidate might still be given admission, but asked to take an English proficiency class and/or pass an additional English test after joining the university.

It is important to note that while the TOEFL score might not carry much weightage in the admission decision, a good score can still be beneficial for the candidate. A high score can demonstrate the candidate's proficiency in English and assure the admission committee that the candidate is capable of handling the coursework and research in English. Additionally, a good TOEFL score might also help the candidate in securing financial aid or scholarships.

In conclusion, while a TOEFL score is usually a requirement for international students applying for graduate studies in the United States, it is not a significant factor in the admission decision. Candidates should aim to clear the cut-off score and focus more on other aspects of the application to make a strong case for their admission.